A Factorization Approach Using Adaptive Proper Orthogonal Decomposition for Kinetics Calculations

A new kinetics calculation method using factorization and proper orthogonal decomposition (POD) is proposed. In the present method, discretized neutron balance equations that have fine and coarse time resolutions are derived using the factorization of the neutron flux. Then dimensionality reduction using POD is applied to the fine time-step calculation. The orthogonal basis for POD is constructed from the flux distributions at the current and previous coarse time steps on the fly. The fine time dependence captured in the fine time-step POD calculation is reflected in the coarse time-step calculation to accurately span the solution space around the next time step. The accuracy and performance of the present method are verified in the TWIGL benchmark problem. The calculation results show that the present method achieved a 26% speedup while maintaining accuracy compared to the conventional multigrid amplitude function method in the present calculation conditions.